Number 3026
Application Note
Se­ries
Electrical Characterization of
Photovoltaic Materials and
Solar Cells with the Model 4200-SCS
Semiconductor Characterization System
I‑V, C‑V, C-f, DLCP, Pulsed I-V, Resistivity, and
Hall Voltage Measurements
Introduction
The increasing demand for clean energy and the largely
untapped potential of the sun as an energy source is making
solar energy conversion technology increasingly important.
As a result, the demand for solar cells, which convert sunlight
directly into electricity, is growing. Solar or photovoltaic (PV)
cells are made up of semiconductor materials that absorb
photons from sunlight and then release electrons, causing an
electric current to flow when the cell is connected to a load.
A variety of measurements are used to characterize a solar
cell’s performance, including its output and its efficiency. This
electrical characterization is performed as part of research and
development of photovoltaic cells and materials, as well as
during the manufacturing process.
Some of the electrical tests commonly performed on solar
cells involve measuring current and capacitance as a function
of an applied DC voltage. Capacitance measurements are
sometimes made as a function of frequency or AC voltage.
Some tests require pulsed current-voltage measurements.
These measurements are usually performed at different light
intensities and under different temperature conditions. A variety
of important device parameters can be extracted from the DC
and pulsed current-voltage (I‑V) and capacitance‑voltage (C‑V)
measurements, including output current, conversion efficiency,
maximum power output, doping density, resistivity, etc. Electrical
characterization is important in determining how to make the
cells as efficient as possible with minimal losses.
Instrumentation such as the Model 4200-SCS Semiconductor
Characterization System can simplify testing and analysis when
making these critical electrical measurements. The Model 4200SCS is an integrated system that includes instruments for making
DC and ultra fast I‑V and C‑V measurements, as well as control
software, graphics, and mathematical analysis capability. The
Model 4200-SCS is well-suited for performing a wide range of
measurements, including DC and pulsed current-voltage (I‑V),
capacitance-voltage (C‑V), capacitance-frequency (C-f), drive level
capacitance profiling (DLCP), four-probe resistivity (ρ, σ), and
Hall voltage (V H) measurements. This application note describes
how to use the Model 4200-SCS to make these electrical
measurements on PV cells.
Making Electrical Measurements
with the Model 4200-SCS
To simplify testing photovoltaic materials and cells, the Model
4200-SCS is supported with a test project for making many of
the mostly commonly used measurements easily. These tests,
which include I‑V, capacitance, and resistivity measurements, also
include formulas for extracting common parameters such as the
maximum power, short circuit current, defect density, etc. The
SolarCell project (Figure 1) is included with all Model 4200-SCS
systems running KTEI Version 8.0 or later. It provides thirteen
tests (Table 1) in the form of ITMs (Interactive Test Modules)
and UTMs (User Test Modules) for electrical characterization.
Table 1. Test modules in the SolarCell project
Subsite Level
IV_sweep
Test Module
fwd-ivsweep
Description
Performs I‑V sweep and calculates Isc,
Voc, Pmax, Imax, Vmax, FF
rev-ivsweep
Performs reversed bias I‑V sweep
CV_sweep
cvsweep
Generates C‑V sweep
C-2vsV
Generates C‑V sweep and calculates 1/C2
cfsweep
Sweeps the frequency and measures
capacitance
DLCP
Measures capacitance as AC voltage is
swept. DC voltage is applied so as to
keep the total applied voltage constant.
The defect density is calculated.
Pulse-IV
pulse-iv-sweep Performs pulse I-V sweep using one
channel of PMU
4PtProbe_resistivity HiR
Uses 3 or 4 SMUs to source current and
measure voltage difference for high
resistance semiconductor materials.
Calculates sheet resistivity.
LoR
Uses 1 or 2 SMUs to source current and
measure voltage using remote sense.
Calculates sheet resistivity. Uses current
reversal method to compensate for
thermoelectric voltage offsets.
vdp_resistivity
I1_V23
First of 4 ITMs that are used to measure
the van der Pauw resistivity. This ITM
sources current between terminals 1 and
4 and measures the voltage difference
between terminals 2 and 3.
I2_V34
Sources current between terminals 2 and
1 and measures the voltage difference
between terminals 3 and 4.
I3_V41
Sources current between terminals 3 and
2 and measures the voltage difference
between terminals 4 and 1.
I4_V12
Sources current between terminals 4 and
1 and measures the voltage difference
between terminals 1 and 2.
DC I-V
C-V
Pulsed I-V
Resistivity
Figure 1. Screenshot of SolarCell project for the Model 4200-SCS
DC Current-Voltage (I‑V) Measurements
Parameters Derived from I‑V Measurements
As described previously, many solar cell parameters can be
derived from current-voltage (I‑V) measurements of the cell.
These I‑V characteristics can be measured using the Model
4200-SCS’s Source-Measure Units (SMUs), which can source
and measure both current and voltage. Because these SMUs
have four-quadrant source capability, they can sink the cell
current as a function of the applied voltage. Two types of SMUs
are available for the Model 4200-SCS: the Model 4200-SMU,
which can source/sink up to 100mA, and the Model 4210-SMU,
which can source/sink up to 1A. If the output current of the cell
exceeds these current levels, it may be necessary to reduce it,
possibly by reducing the area of the cell itself. However, if this
is not possible, Keithley’s Series 2400 or 2600A SourceMeter®
instruments, which are capable of sourcing/sinking higher
currents, offer possible alternative solutions.
A solar cell may be represented by the equivalent circuit
model shown in Figure 2, which consists of a light-induced
current source (IL), a diode that generates a saturation current
[IS(eqV/kT –1)], series resistance (rs), and shunt resistance (rsh).
The series resistance is due to the resistance of the metal
contacts, ohmic losses in the front surface of the cell, impurity
concentrations, and junction depth. The series resistance is an
important parameter because it reduces both the cell’s shortcircuit current and its maximum power output. Ideally, the series
resistance should be 0W (rs = 0). The shunt resistance represents
the loss due to surface leakage along the edge of the cell or to
crystal defects. Ideally, the shunt resistance should be infinite
(rsh = ∞).
If a load resistor (R L) is connected to an illuminated solar
cell, then the total current becomes:
I = IS(eqV/kT – 1) – IL
where: IS = current due to diode saturation
IL = current due to optical generation
rs
PV Cell
Photon hυ
IL
rsh
Figure 2. Idealized equivalent circuit of a photovoltaic cell
Load RL
Several parameters are used to characterize the efficiency of
the solar cell, including the maximum power point (Pmax), the
energy conversion efficiency (η), and the fill factor (FF). These
points are illustrated in Figure 3, which shows a typical forward
bias I‑V curve of an illuminated PV cell. The maximum power
point (Pmax) is the product of the maximum cell current (Imax)
and the voltage (Vmax) where the power output of the cell is
greatest. This point is located at the “knee” of the curve.
I sc
Cell Current (mA)
Imax
SMU1
A
Force HI
Pmax
200
Sense HI
150
V-Source
V
Solar Cell
100
Maximum Power Area
Pmax = ImaxVmax
Sense LO
50
Force LO
0
0.0
0.2
0.4
0.6
Cell Voltage (V)
0.8
Vmax Voc
Figure 3. Typical forward bias I‑V characteristics of a PV cell
The fill factor (FF) is a measure of how far the I‑V
characteristics of an actual PV cell differ from those of an ideal
cell. The fill factor is defined as:
ImaxVmax
FF =_____________
IscVoc
where:
Imax = the current at the maximum power output (A)
Vmax= the voltage at the maximum power output (V)
Isc = the short-circuit current (A)
Voc = the open-circuit voltage (V)
As defined, the fill factor is the ratio of the maximum power
(Pmax = ImaxVmax) to the product of the short circuit current (Isc)
and the open circuit voltage (Voc). The ideal solar cell has a fill
factor equal to one (1) but losses from series and shunt resistance
decrease the efficiency.
Another important parameter is the conversion efficiency (η),
which is defined as the ratio of the maximum power output to
the power input to the cell:
Pmax
η = _______
Pin
where:
Pmax= the maximum power output (W)
Pin = the power input to the cell defined as the total radiant
energy incident on the surface of the cell (W)
Making Connections to the Solar Cell
for I‑V Measurements
Figure 4 illustrates a solar cell connected to the Model 4200-SCS
for I‑V measurements. One side of the solar cell is connected
to the Force and Sense terminals of SMU1; the other side is
connected to the Force and Sense terminals of either SMU2 or
the ground unit (GNDU) as shown.
SMU2 or GNDU
Figure 4. Connection of Model 4200-SCS to a solar cell for I‑V measurements
Using a four-wire connection eliminates the lead resistance
that would otherwise affect this measurement’s accuracy.
With the four-wire method, a voltage is sourced across the
solar cell using one pair of test leads (between Force HI and
Force LO), and the voltage drop across the cell is measured
across a second set of leads (across Sense HI and Sense LO).
The sense leads ensure that the voltage developed across the
cell is the programmed output value and compensate for the
lead resistance.
Forward-Biased I‑V Measurements
Forward-biased I‑V measurements of the solar cell are made
under controlled illumination. The SMU is set up to output a
voltage sweep and measure the resulting current. This forward
bias sweep can be performed using the “fwd-ivsweep” ITM,
which allows adjusting the sweep voltage to the desired values.
As previously illustrated in Figure 3, the voltage source is swept
from V1 = 0 to V2 = VOC. When the voltage source is 0 (V1 = 0),
the current is equal to the source-circuit current (I1 = ISC).
When the voltage source is an open circuit (V2 = VOC), then
the current is equal to zero (I2 = 0). The parameters, VOC and
ISC, can easily be derived from the sweep data using the Model
4200-SCS’s built-in mathematical analysis tool, the Formulator.
For convenience, the SolarCell project has the commonly derived
parameters already calculated, so the values automatically
appear in the Sheet tab every time the test is executed. Figure 5
shows some of the derived parameters in the Sheet tab. These
parameters include the short-circuit current (ISC), the open
circuit voltage (VOC), the maximum power point (Pmax), the
maximum cell current (Imax), the maximum cell voltage (Vmax),
and the fill factor (FF).
Th user can easily add other formulas depending on the
required parameters that need to be determined.
Using the Formulator, the conversion efficiency (η) can also
be calculated if the user knows the power input to the cell and
inputs the formula. The current density (J) can also be derived
by using the Formulator and inputting the area of the cell.
Figure 5. Results of calculated parameters shown in Sheet tab
Figure 6 shows an actual I‑V sweep of an illuminated
silicon PV cell generated with the Model 4200-SCS using the
“fwd-ivsweep” ITM. Because the system’s SMUs can sink current,
the curve passes through the fourth quadrant and allows power
to be extracted from the device (I–, V+). If the current output
spans several decades as a function of the applied voltage, it
may be desirable to generate a semilog plot of I vs. V. The Graph
tab options support an easy transition between displaying data
graphically on either a linear or a log scale.
go to the Graph Settings tab, select Axis Properties, select the
Y1 Axis tab, and click on the Invert checkbox. The inverse of the
graph will appear as shown in Figure 7.
Figure 7. Inversion of the forward-biased I‑V curve about the voltage axis
Figure 6. I‑V sweep of silicon PV cell generated with the 4200-SMU
If desired, the graph settings functions make it easy to create
an inverted version of the graph about the voltage axis. Simply
The series resistance (rs) can be determined from the forward
I‑V sweep at two or more light intensities. First, make I‑V curves
at two different intensities (the magnitudes of the intensities
are not important). Measure the slope of this curve from the
far forward characteristics where the curve becomes linear. The
inverse of this slope yields the series resistance:
∆V
rs = ____
∆I
By using additional light intensities, this technique can be
extended using multiple points located near the knee of the
curves. As illustrated in Figure 8, a line is generated from which
the series resistance can be calculated from the slope.
Current (mA)
When considered as ammeters, one important feature of the
Model 4200-SCS’s SMUs is their very low voltage burden. The
voltage burden is the voltage drop across the ammeter during the
measurement. Most conventional digital multimeters (DMMs) will
have a voltage burden of at least 200mV at full scale. Given that
only millivolts may be sourced to the sample in solar cell testing,
this can cause large errors. The Model 4200-SCS’s SMUs don’t
produce more than a few hundred microvolts of voltage burden,
or voltage drop, in the measurement circuit.
rS =
VReverse Bias
Linear region used
∆VReverse Bias
rsh ≈
to estimate rsh
∆IReverse Bias
∆VReverse Bias
∆IReverse Bias
log IReverse Bias
Figure 9. Typical reverse-biased characteristics of a PV cell
Figure 10 shows an actual curve of a reverse-biased solar cell,
generated using the ITM “rev-ivsweep”. In this semi-log graph,
the absolute value of the current is plotted as a function of the
reverse-biased voltage that is on an inverted x-axis.
∆V
∆I
Voltage (V)
Figure 8. Slope method used to calculate the series resistance
Reverse-Biased I‑V Measurements
The leakage current and shunt resistance (rsh) can be derived
from the reverse-biased I‑V data. Typically, the test is performed
in the dark. The voltage is sourced from 0V to a voltage level
where the device begins to break down. The resulting current
is measured and plotted as a function of the voltage. Depending
on the size of the cell, the leakage current can be as small as
picoamps. The Model 4200-SCS has a preamp option that allows
making accurate measurements well below a picoamp. When
making very sensitive low current measurements (nanoamps
or less), use low noise cables and place the device in a shielded
enclosure to shield it electrostatically. This conductive shield is
connected to the Force LO terminal of the Model 4200-SCS. The
Force LO terminal connection can be made from the outside
shell of the triax connectors, the black binding post on the
ground unit (GNDU), or from the Force LO triax connector on
the GNDU.
One method for determining the shunt resistance of the PV
cell is from the slope of the reverse-biased I‑V curve, as shown
in Figure 9. From the linear region of this curve, the shunt
resistance can be calculated as:
∆VReverse Bias
rsh = _______________
∆ IReverse Bias
Figure 10. Reverse-biased I‑V measurement of silicon solar cell using the
Model 4200‑SMU
Capacitance Measurements
Capacitance-voltage measurements are useful in deriving
particular parameters about PV devices. Depending on the type
of solar cell, capacitance-voltage (C‑V) measurements can be
used to derive parameters such as the doping concentration
and the built-in voltage of the junction. A capacitance-frequency
(C-f) sweep can be used to provide information on the existence
of traps in the depletion region. The Model 4210-CVU, the
Model 4200-SCS’s optional capacitance meter, can measure
the capacitance as a function of an applied DC voltage (C‑V), a
function of frequency (C-f), a function of time (C-t), or a function
of the AC voltage. The Model 4210-CVU can also measure
conductance and impedance.
To make capacitance measurements, a solar cell is
connected to the Model 4210-CVU as shown in Figure 11.
Like I‑V measurements made with the SMU, the capacitance
measurements also involve a four-wire connection to compensate
for lead resistance. The HPOT/HCUR terminals are connected to
the anode and the LPOT/LCUR terminals are connected to the
cathode. This connects the high DC voltage source terminal of
the Model 4210-CVU to the anode.
4210-CVU
AC
Source
HCUR
HPOT
AC
Voltmeter
Solar
Cell
LPOT
ABB
Feedback
AC
Ammeter
LCUR
Figure 12. C‑V sweep of a silicon solar cell
Figure 11. Connecting the solar cell to the Model 4210-CVU capacitance meter
Figure 11 shows the shields of the four coax cables coming
from the four terminals of the capacitance meter. The shields
from the coax cables must be connected together as close as
possible to the solar cell to obtain the highest accuracy because
this reduces the effects of the inductance in the measure circuit.
This is especially important for capacitance measurements made
at higher test frequencies.
Performing an Open and Short Connection Compensation
will reduce the effects of cable capacitance on measurement
accuracy. This simple procedure is described in Section 15 of the
Model 4200-SCS Reference Manual.
Given that the capacitance of the cell is directly related to
the area of the device, it may be necessary to reduce the area of
the cell itself, if possible, to avoid capacitances that may be too
high to measure. Also, setting the Model 4210-CVU to measure
capacitance at a lower test frequency and/or lower AC drive
voltage will allow measuring higher capacitances.
C‑V Sweep
C‑V measurements can be made either forward-biased or reversebiased. However, when the cell is forward-biased, the applied
DC voltage must be limited; otherwise, the conductance may get
too high for the capacitance meter to measure. The maximum
DC current cannot be greater than 10mA; otherwise, the
instrument’s DC voltage source will go into compliance and the
DC voltage output will not be at the desired level.
Figure 12 illustrates a C‑V curve of a silicon solar cell
generated by the Model 4210-CVU using the “cvsweep”
ITM. This test was performed in the dark while the cell was
reversed-biased.
Rather than plotting dC/dV, it is sometimes desirable to view
the data as 1/C2 vs. voltage because some parameters are related
to the 1/C2 data. For example, the doping density (N) can be
derived from the slope of this curve because N is related to the
capacitance by:
Figure 13. 1/C 2 vs. voltage of a silicon solar cell
2
N(a) = ______________________
qES A2[d(1/C2)/dV]
where:
N(a)= the doping density (1/cm3)
q = the electron charge (1.60219 × 10 –19C)
Es = semiconductor permittivity (1.034 × 10 –12F/cm for silicon)
A = area (cm2)
C = measured capacitance (F)
V = applied DC voltage (V)
The built-in voltage of the cell junction can be derived from
the intersection of the 1/C2 curve and the horizontal axis. This
plot should be a fairly straight line. An actual curve taken with
the Model 4210-CVU, generated using the “C-2vsV” ITM, is shown
in Figure 13. The Formulator function is used to derive both
the doping density (N) and the built-in voltage on the x-axis
(x-intercept). The doping density is calculated as a function of
voltage in the Formulator and appears in the Sheet tab in the
ITM. The user must input the area of the cell in the Constants
area of the Formulator. The built-in voltage source value is
derived both in the Formulator and by using a Linear Line Fit
option in the Graph settings. Notice the value of the x-intercept
appears in the lower left corner of the graph.
C-f Sweep
The Model 4210-CVU option can also measure capacitance,
conductance, or impedance as a function of the test frequency.
The range of frequency is from 1kHz to 10MHz. The curve
in Figure 14 was generated by using the “cfsweep” ITM. Both
the range of sweep frequency and the bias voltage can be
adjusted. The desired parameters, such as the trap densities,
can be extracted from the capacitance vs. frequency data. The
measurements can be repeated at various temperatures.
The test frequency and temperature of the measurement can also
be varied to show a profile that is energy dependent.
Once the measurements are taken, a quadratic fit of the C‑V
data is related to the impurity density at a given depletion depth
as follows for a p-type semiconductor:
NDL ≡
E V + Ee
ρ
C 03
= e = p + ∫ 0 g ( E , xe )dE
2
EF
2 qε A C 1
q
where:
NDL = defect density (cm–3)
C1, C0 = coefficients of quadratic fit of C‑V data
q
= electron charge (1.60 × 10 –19C)
ε
= permittivity (F/cm)
A
= area of solar cell (cm2)
ρe
= charge density (C/cm3)
p
= hole density (cm–3)
xe = distance from interface where EF – Ev = Ee
The coefficients C0 and C1 are determined via a full leastsquares best fit of the data to a quadratic equation:
dQ/dV = C2 (dV)2 + C1*(dV) + C0
However, only the C0 and C1 coefficients are used in the analysis.
Figure 14. C-f Sweep of Solar Cell
Drive Level Capacitance Profiling (DLCP)
Drive Level Capacitance Profiling (DLCP) is a technique for
determining the defect density (NDL) as a function of depth of a
photovoltaic cell1. During the DLCP measurement, the applied
AC voltage (peak-to-peak) is swept and the DC voltage is varied
while the capacitance is measured. This is in contrast to the
conventional C‑V profiling technique, in which the AC rms
voltage is fixed and the DC voltage is swept.
In DLCP, the DC voltage is automatically adjusted to keep the
total applied voltage (AC + DC) constant while the AC voltage is
swept. By maintaining a constant total bias, the exposed charge
density (ρe) inside the material stays constant up to a fixed
location (xe), which is defined as the distance from the interface
where EF – Ev = Ee. This is also in contrast to conventional C‑V
profiling, the analysis of which assumes that the only charge
density changes occur at the end of the depletion region.1
Thus, in DLCP, the position (xe) can be varied by adjusting the
DC voltage bias to the sample. This also allows determining the
defect density as a function of the distance, or special profiling.
1 J. T. Heath, J. D. Cohen, W. N. Shafarman, “Bulk and metastable defects in CuIn1–xGa xSe2
thin films using drive-level capacitance profiling,” Journal of Applied Physics, vol. 95, no.
3, p. 1000, 2004
The “DLCP” UTM allows making C‑V measurements for drive
level capacitance profiling. During these measurements, the
total applied voltage remains constant as the DC voltage bias is
automatically adjusted as the AC voltage drive level amplitude
varies. The AC amplitude of the 4210-CVU can vary from 10mVrms
to 100mVrms (14.14mV to 141.4mVp-p). The range of frequency can
also be set from 1kHz to 10MHz. The capacitance is measured as
the AC voltage is sweeping.
Table 2 lists the input parameters used in the UTM, the
allowed range of input values, and descriptions. The user
inputs the total applied voltage (VmaxTotal), the AC start, stop,
and step voltages (VacppStart, VacppStop, and VacppStep), the
time between voltage steps (SweepDelay), the test frequency
(Frequency), the measurement speed (Speed), the measurement
range (CVRange), and offset compensation (OpenComp,
ShortComp, LoadComp, and LoadVal).
Table 2. Adjustable parameters for the DLCP UTM
Parameter
VmaxTotal
VacppStart
VacppStop
VacppStep
SweepDelay
Frequency
Speed
CVRange
OpenComp
ShortComp
LoadComp
LoadVal
Range
–10 to 10 volts
.01414 to .1414
.02828 to .1414
.0007070 to .1414
0 to 100
1E+3 to 10E+6
0, 1, 2
0, 1E–6, 30E–6,
1E–3
1, 0
1, 0
1, 0
1 to 1E+9
Description
Applied DC Volts and ½ AC Volts p-p
Start Vac p-p
Stop Vac p-p
Step Vac p-p
Sweep delay time in seconds
Test Frequency in Hertz
0=Fast, 1=Normal, 2=Quiet
0=autorange, 1µA, 30µA, 1mA
Enables/disables open compensation for CVU
Enables/disables short compensation for CVU
Enables/disables load compensation for CVU
Load value
Once the test is executed, the capacitance, AC voltage, DC
voltage, time stamp, frequency, and the defect density (NDL)
are determined and their values are listed in the Sheet tab. The
defect density is calculated in the Formulator using a quadratic
line fit of the C‑V data. The coefficients (C0 and C1) of the
quadratic equation are also listed in the Sheet tab. The user
inputs the area and permittivity of the solar cell to be tested into
the Constants/Values/Units area of the Formulator.
the other side of the cell is connected to the shield of the coax
cable, which is the LO terminal of the PMU.
Solar Cell
Connection to
common terminal
SMA Coax
Cable
Figure 15 shows the measurement results in the graph of
capacitance vs. AC voltage p-p. Notice the coefficients of the
derived quadratic line fit and the defect density are displayed on
the graph.
A
The capacitance measurements can be repeated at various
applied total voltages in order to vary the position of xe. The
energy (Ee) can be varied by changing the test frequency (1kHz
to 10MHz) or the temperature. To change the temperature of the
measurement, the user can add a User Test Module (UTM) to
control a temperature controller via the Model 4200-SCS’s GPIB
interface. The Model 4200-SCS is provided with user libraries for
operating the Temptronics and Triotek temperature controllers.
A
V
50Ω
CH1
V
50Ω
4225-PMU
CH2
Figure 16. Connecting the solar cell to the Model 4225-PMU Ultra-Fast
I-V Module
Unlike the DC I-V and C-V measurements, the 4225-PMU uses
a two-wire technique. The Short Compensation feature can be
used to “zero out” the voltage drops due to the cables so that a
4-wire measurement technique isn’t necessary.
Because solar cells are fairly capacitive, it is important to
ensure the pulse width is long enough for the pulsed I-V sweep.
The waveform capture mode should be used to verify the pulse
width prior to generating the pulsed I-V sweep. The waveform
capture mode enables a time-based current and/or voltage
measurement that is typically the capture of a pulsed waveform.
This can be used to perform a dynamic test on the cell or used
as a diagnostic tool for choosing the appropriate pulse settings
Figure 15. Capacitance vs. AC voltage p-p of a solar cell
Pulsed I-V Measurements
Pulsed I-V measurements can be useful for studying parameters
of solar cells. In particular, pulsed I-V measurements have been
used to determine the conversion efficiency, minimum carrier
lifetime, and the effects of cell capacitance. The Model 4225-PMU,
the Model 4200-SCS’s optional Ultra-Fast I-V Module, can output
pulsed voltage and measure current, and can capture ultrahigh-speed current or voltage waveforms in the time domain. In
addition to sourcing a pulsed voltage, the PMU can sink current
so it can measure a solar cell’s current output.
To make pulsed I-V measurements on a solar cell, the Model
4225-PMU is connected to the cell as shown in Figure 16. Each
PMU has two channels so the solar cell can be connected using
either one or two channels. In the one-channel case shown, one
end of the cell is connected to the HI terminal of PMU CH1 and
Figure 17. Pulsed I-V measurement on solar cell using Model 4225-PMU
in the pulsed I-V mode. Given that larger solar cells have larger
capacitances, it may be necessary to reduce the area of the cell
itself to avoid a long settling time in the measurement.
The results of generating a pulsed I-V measurement sweep on
a silicon solar cell are shown in Figure 17. Note that the current
is in the fourth quadrant of the curve. This indicates that the
PMU is sinking current; in other words, the current is flowing
out of the solar cell and into the PMU.
Resistivity and Hall Voltage Measurements
Determining the resistivity of a solar cell material is a common
electrical measurement given that the magnitude of the resistivity
directly affects the cell’s performance. Resistivity measurements
of semiconductor materials are usually performed using a
four-terminal technique. Using four probes eliminates errors
due to the probe resistance, spreading resistance under each
probe, and the contact resistance between each metal contact
and the semiconductor material. Two common techniques for
determining the resistivity of a solar cell material are the fourpoint collinear probe method and the van der Pauw method.
The SolarCell project contains several ITMs for making both
types of measurements. More detailed information about making
resistivity measurements on semiconductor materials using
the Model 4200-SCS can be found in Keithley Application Note
#2475, “Four-Probe Resistivity and Hall Voltage Measurements
with the Model 4200-SCS.”
Four-Point Collinear Probe Measurement Method
The four-point collinear probe technique involves bringing four
equally spaced probes in contact with a material of unknown
resistance. The probe array is placed in the center of the material
as shown in Figure 18. The two outer probes are used to source
current and the two inner probes are used to measure the
resulting voltage difference across the surface of the material.
Current
Source
Voltmeter
Figure 18. Four-point collinear probe resistivity configuration
From the sourced current and the measured voltage, the
surface or sheet resistivity is calculated by:
p V
σ = ____ ×___
ln2 I
where:
σ= surface resistivity (W/ ■)
V = the measured voltage (V)
I = the source current (A)
Note that the units for sheet resistivity are expressed as ohms
per square (W/ ■) in order to distinguish this number from the
measured resistance (V/I), which is simply expressed in ohms.
Correction factors to the resistivity calculation may be required
for extremely thin or thick samples or if the diameter of the
sample is small relative to the probe spacing.
If the thickness of the sample is known, the volume resistivity
can be calculated as follows:
p V
ρ = ____ ×___ × t × k
ln2 I
where:
ρ= volume resistivity (W-cm)
t = the sample thickness (cm)
k = a correction factor* based on the ratio of the probe spacing
to wafer diameter and on the ratio of wafer thickness to
probe spacing
*The correction factors can be found in a standard four-point
probe resistivity test procedure such as Semi MF84: Standard
Test Method for Measuring Resistivity of Silicon Wafers With
an In-Line Four-Point Probe. This standard was originally
published by ASTM International as ASTM F 84.
Using the Four-Point Probe ITMs, HiR and LoR
The “HiR” and “LoR” ITMs are both used for making four-point
collinear probe measurements. The “HiR” ITM can be used
for materials over a wide resistance range, ~1mW to 1TW.
The Model 4200-PA preamps are required for making high
resistance measurements (>1MW). The “LoR” ITM is intended for
measurements of lower resistance materials (~1mW–1kW).
A screenshot of the “HiR” ITM for measuring four-probe
resistivity is shown in Figure 19.
The “HiR” ITM uses either three or four SMUs to make the
resistivity measurements. One SMU (SMU1) and the ground
unit (GNDU) are used to source current between the outer
two probes. Two other SMUs (SMU2 and SMU3) are used to
measure the voltage drop between the two inner probes. The
Force HI terminal of each SMU is connected to each of the four
probes. The SMU designation for this configuration is shown in
Figure 20.
In the Formulator, the voltage difference between SMU2 and
SMU3 is calculated and the resistance and sheet resistivity are
derived from the voltage difference. The results appear in the
Sheet tab of the ITM.
When making high resistance measurements, potential
sources of error need to be considered in order to make optimal
measurements. Use a probe head that has a level of insulation
resistance between the probes that is sufficiently higher than
Figure 19. “HiR” test module for measuring resistivity
the resistance of the material to be measured. This will help
prevent errors due to leakage current through the probe head.
Ensure that the measurement circuit is electrostatically shielded
by enclosing the circuit in a metal shield. The shield is connected
to the LO terminal of the 4200. The LO terminal is located on
the GNDU or on the outside shell of the triax connectors. Use
triax cables to produce a guarded measurement circuit. This will
prevent errors due to leakage current and significantly reduce
the test time. Finally, the Model 4200-PA preamp option is
required to source very small currents (nanoamp and picoamp
range) and to provide high input impedance (>1E16 ohms) to
avoid loading errors when measuring the voltage difference.
The “LoR” ITM is only used for lower resistance materials and
requires only one or two SMUs. In this case, the Force and Sense
terminals of the SMUs are connected to the four-point probe as
shown in Figure 20.
Using the Formulator,
calculate the voltage
difference between
SMU2 and SMU3.
SMU1: Set to Current
Bias (VMU) – Set
current level to have
about a 10mV drop
between SMU2 and
SMU3.
SMU2: Set to Current
Bias (VMU) – Use as
high impedance voltmeter, and set
current to 0A on 1nA
range.
SMU3: Set to Current
Bias (VMU) – Use as
high impedance voltmeter, and set
current to 0A on 1nA
range.
GNDU: Common
connection for all
SMUs. Or, this can be
SMU4 set to
Common.
Force HI
Force HI
Force HI
Force HI
Figure 20. SMU designation for four-point collinear probe measurements
SMU2 or GNDU
SMU1
Sense HI
Sense HI
Force HI
Force HI
1
2
3
4
Figure 21. Connecting two SMUs for four-point probe measurements
In the configuration shown in Figure 21, the Force HI
terminal SMU1 sources the current through Probe 1. The voltage
difference between Probes 2 and 3 is measured through the
Sense terminals of the two SMUs.
To compensate for thermoelectric offset voltages, two voltage
measurements are made with currents of opposite polarity.
The two measurements are combined and averaged to cancel
the thermoelectric EMFs. The “LoR” ITM performs this offset
correction automatically by sourcing the two current values in
the List Sweep and then mathematically correcting for the offsets
V5
1
2
1
2
1
2
1
2
4
3
4
3
4
3
V3
4
3
V7
V1
V6
1
2
1
2
1
2
1
2
4
3
4
3
4
3
V4
4
3
V8
V2
Figure 22. Van der Pauw resistivity measurement conventions
in the Formulator. The corrected resistance and sheet resistivity
are displayed in the Sheet tab.
A plot of this function is shown in Figure 23. The value of “f”
can be found from this plot once Q has been calculated.
Measuring Resistivity with the van der Pauw Method
1.0
The van der Pauw (vdp) technique for measuring resistivity
uses four isolated contacts on the boundary of a flat,
arbitrarily shaped sample. The resistivity is derived from eight
measurements made around the sample as shown in Figure 22.
Once all the voltage measurements have been taken, two
values of resistivity, ρA and ρB, are derived as follows:
p (V2 + V4 – V1 – V3)
ρ = ____ fAts________________________
A ln2
4I
0.9
0.8
f
0.7
0.6
0.5
p (V6 + V8 – V5 – V7)
ρB = ____ fBts________________________
ln2
4I
0.4
where:
ρA and ρB are volume resistivities in ohm-cm;
ts is the sample thickness in cm;
V1–V8 represent the voltages measured by the voltmeter;
I is the current through the sample in amperes;
f A and f B are geometrical factors based on sample symmetry, and
are related to the two resistance ratios QA and QB as shown in
the following equations (f A = f B = 1 for perfect symmetry).
1
10
100
Q
Figure 23. Plot of f vs. Q
Once ρA and ρB are known, the average resistivity (ρAVG) can
be determined as follows:
ρA + ρB
ρAVG =__________
2
QA and QB are calculated using the measured voltages as
follows:
Using the vdp_resistivity subsite and
vdp method ITMs
V2 – V1
Q = __________
A
V4 – V3
To automate the vdp resistivity measurements, the SolarCell
project has a vdp-resistivity subsite with four ITMs: “I1_V23”,
“I2_V34”, “I3_V41”, and “I4_V12.” A screenshot of the test is shown
in Figure 24.
V6 – V5
Q = __________
B
V8 – V7
Also, Q and f are related as follows:
(
Q – 1 _______
f
e0.693/f
________
=
arc cosh _______
Q + 1 0.693
2
)
Each terminal of the sample is connected to the Force HI
terminal of an SMU, so a Model 4200-SCS with four SMUs is
required. The four SMUs are configured differently in each
of the four ITMs – one SMU supplies the test current, two
Figure 24. Screenshot of van der Pauw test
are configured as voltmeters, and one is set to common. This
measurement setup is repeated around the sample, with each
of the four SMUs serving a different function in each of the four
ITMs. A diagram of the function of each SMU in each ITM is
shown in Figure 25.
Adjusting the Test Parameters
Before executing the test, some of the test parameters must be
adjusted based on the sample to be tested. In particular, it’s
necessary to specify the source current, the settling time, and the
thickness of the material.
ITM NAME:
I2_V34
Common
Current Bias (+)
SMU1
SMU2
ITM NAME:
I4_V12
Common
Current Bias (–)
SMU1
SMU2
Voltmeter
Voltmeter
SMU1
SMU2
V12
SMU1
SMU2
V12
2
1
2
1
2
1
2
4
3
4
3
4
3
4
3
SMU4
SMU3
V34
Voltmeter
SMU4
SMU3
V34
Voltmeter
Voltmeter
SMU4
SMU3
Current Bias (+)
Common
ITM NAME:
I3_V41
Voltmeter
Common
SMU2
SMU1
1
Voltmeter
Common
SMU2
SMU1
1
Current Bias (+)
Voltmeter
SMU1
2
SMU2
1
3
SMU3
3
SMU4
Voltmeter
Voltmeter
SMU1
SMU2
1
2
4
3
V23
4
Current Bias (+)
SMU3
Common
Current Bias (–)
2
V41
4
SMU4
Current Bias (–)
ITM NAME:
I1_V23
2
V41
SMU4
Voltmeter
1
Voltmeter
Voltmeter
Voltmeter
4
SMU3
Current Bias (–)
Figure 25. SMU configurations for van der Pauw measurements
SMU4
Common
V23
3
SMU3
Voltmeter
SMU4
Common
SMU3
Voltmeter
Input Source Current: Before running the project, input the
current source values based on the expected sample resistance.
Adjust the current so that the voltage difference will not exceed
approximately 25mV to keep the sample in thermal equilibrium.
In each of the four ITMs, enter both polarities of the test current.
The same magnitude must be used for each ITM.
Input the Settling Time: For high resistance samples, it will be
necessary to determine the settling time of the measurements.
This can be accomplished by creating an ITM that sources
current into two terminals of the samples and measures the
voltage drop on the adjacent two terminals. The settling time
can be determined by taking multiple voltage readings and then
graphing the voltage difference as a function of time.
This settling time test can be generated by copying and
then modifying one of the existing vdp ITMs. Switch the source
function from the sweep mode to the sampling mode. Then, in
the Timing menu, take a few hundred or so readings with a delay
time of one second. Make sure that the “Timestamp Enabled”
box is checked. After the readings are done, plot the voltage
difference vs. time on the graph. The settling time is determined
by observing the graph and finding the time when the reading is
within the desired percentage of the final value.
Input the Thickness of the Sample: Enter the thickness of the
sample into the Calc sheet at the subsite level. Select the subsite
vdp_resistivity. Go to the Subsite Data vdp-device tab. It contains
Figure 26. Executing the vdp_resistivity test
the output values of the voltage differences and test current.
From the Calc tab, the thickness can be adjusted. The default
thickness is 1cm.
Input Correction Factor: The resistivity formula found in the
Calc sheet at the subsite level also allows inputting a correction
factor, if necessary. The resistivity is multiplied by this number,
which may be based on the geometry or uniformity of the
sample. By default, the correction factor is 1.
Running the Project
The van der Pauw resistivity measurements must be run at the
subsite level. Make sure that all four checkboxes in front of the
vdp ITMs (“I1_V23,” “I2_V34,” “I3_V41,” and “I4_V12”) are checked
and then click on the subsite vdp_resistivity. Execute the project
by using the subsite Run button (circular arrow). Each time the
test is run, the subsite data is updated. The voltage differences
from each of the four ITMS will appear in the Subsite Data
vdp-device Sheet tab. The resistivity will appear in the Subsite
Data Calc sheet as shown in Figure 26.
Hall Voltage Measurements
Hall effect measurements are important to semiconductor
material characterization because the conductivity type, carrier
density, and Hall mobility can be derived from the Hall voltage.
With an applied magnetic field, the Hall voltage can be measured
using the configuration shown in Figure 27.
Once R HC and R HD have been calculated, the average Hall
coefficient (R HAVG) can be determined as follows:
B+
RHC + RHD
RHAVG = ______________
2
i
1
From the resistivity (ρAVG) and the Hall coefficient (R H), the
Hall mobility (µH) can be calculated:
2
4
|RH|
µH = ______
ρAVG
3
t
Using the Model 4200-SCS to Measure
the Hall Voltage
V2–4+
Figure 27. Hall voltage measurement
With a positive magnetic field (B–), apply a current between
Terminals 1 and 3 of the sample, and measure the voltage drop
(V2–4+) between Terminals 2 and 4. Reverse the current and
measure the voltage drop (V4–2+). Next, apply current between
Terminals 2 and 4, and measure the voltage drop (V1–3+)
between Terminals 1 and 3. Reverse the current and measure the
voltage drop (V3–1+) again.
Reverse the magnetic field (B–) and repeat the procedure,
measuring the four voltages: (V2–4–), (V4–2–), (V1–3–), and (V3–1–).
Table 3 summarizes the Hall voltage measurements.
Table 3. Summary of Hall Voltage Measurements
Voltage
Designation
V2–4+
V4–2+
V1–3+
V3–1+
V2–4–
V4–2–
V1–3–
V3–1–
Magnetic
Flux
B+
B+
B+
B+
B–
B–
B–
B–
Current Forced
Between Terminals
1–3
3–1
2–4
4–2
1–3
3–1
2–4
4–2
Voltage Measured
Between Terminals
2–4
4–2
1–3
3–1
2–4
4–2
1–3
3–1
From the eight Hall voltage measurements, the average Hall
coefficient can be calculated as follows:
t(V4–2+ – V2–4+ + V2–4– – V4–2–)
R = _______________________________________
HC
BI
t(V3–1+ – V1–3+ + V1–3– – V3–1–)
R = _______________________________________
HD
BI
where:
R HC and R HD are Hall coefficients in cm3/C;
t is the sample thickness in cm;
V represents the voltages measured in V;
I is the current through the sample in A;
B is the magnetic flux in Vs/cm2
The SolarCell project does not include a specific test to measure
the Hall voltage; however, four ITMs can be added to the subsite
for determining the Hall coefficient and mobility. Given that the
configuration for the Hall measurements is very similar to the
van der Pauw resistivity measurements, the vdp ITMs can be
copied and modified for making the Hall voltage measurements.
The modifications involve changing the functions of the SMUs.
Figure 28 illustrates how to configure the four SMUs in the ITMs
to measure the Hall voltage. Use the Output Value checkboxes on
the Definition tab to return the Hall voltages to the subsite-level
Calc sheet.
User Test Modules (UTMs) must be added to control the
magnet. For a GPIB-controlled electromagnet, users can write a
program using KULT (the Keithley User Library Tool) to control
the magnitude and polarity of the electromagnet. The code
can be opened up in a UTM within the project. Information on
writing code using KULT is provided in Section 8 of the Model
4200-SCS Reference Manual.
If a permanent magnet is used, UTMs can be employed to
create a Project Prompt that will stop the test sequence in the
project tree and instruct the user to change the polarity of the
magnetic field applied to the sample. A Project Prompt is a dialog
window that pauses the project test sequence and prompts
the user to perform some action. See Section A of the Model
4200-SCS Reference Manual for a description of how to use
Project Prompts.
Finally, the Hall coefficient and mobility can be derived in the
subsite-level Calc sheet. These math functions can be added to
the other equations for determining resistivity.
Conclusion
Measuring the electrical characteristics of a solar cell is critical
for determining the device’s output performance and efficiency.
The Model 4200-SCS simplifies cell testing by automating the
I‑V, C‑V, pulsed I-V, and resistivity measurements and provides
graphics and analysis capability. For measurements of currents
greater than 1A, Keithley offers Series 2400 and Series 2600
SourceMeter instruments that can be used for solar cell testing.
Information on these models and further information on making
solar cell measurements can be found on Keithley’s website:
www.keithley.com.
B+
Current Bias (+)
Voltmeter
SMU1
Current Bias (–)
Voltmeter
SMU1
SMU2
SMU2
1
2
1
2
4
3
4
3
SMU4
Voltmeter
SMU3
SMU4
Common
Voltmeter
Voltage Measured: V2–4+
SMU3
V34
Common
Voltage Measured: V4–2+
B+
Voltmeter
Current Bias (+)
Voltmeter
SMU2
SMU1
1
Current Bias (–)
SMU2
SMU1
2
V41
1
2
4
3
V41
4
3
SMU4
SMU3
Common
SMU4
Voltmeter
SMU3
Common
Voltage Measured: V1–3+
Voltmeter
Voltage Measured: V3–1+
B–
Current Bias (+)
SMU1
V12
Voltmeter
SMU2
Current Bias (–)
Voltmeter
SMU2
SMU1
V12
1
2
1
2
4
3
4
3
SMU4
SMU3
Voltmeter
SMU4
Common
SMU3
Voltmeter
Voltage Measured: V2–4–
Common
Voltage Measured: V4–2–
B–
Voltmeter
SMU1
SMU4
Common
Current Bias (+)
SMU2
Voltmeter
SMU1
Current Bias (–)
SMU2
1
2
1
2
4
3
4
3
SMU3
Voltmeter
Voltage Measured: V1–3+
SMU4
Common
SMU3
Voltmeter
Voltage Measured: V3–1–
Figure 28. SMU configurations for Hall voltage measurements
Specifications are subject to change without notice.
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Printed in the U.S.A.
No. 3026
06.02.10